The invention is based on an overpressure valve for packaging containers as defined hereinafter. In a valve of this type, known for instance from German Offenlegungsschrift 35 26 586; U.S. Pat. No. 4,653,661, the strips of adhesive, which are disposed in the region of the peripheral zones of the membrane and define the adhesive-free zone, have a rectangular cross section, with a thickness corresponding approximately to that of the membrane. As a result, when the valve is closed, or in other words when the adhesive-free zone of the membrane rests sealingly on the congruent part of the package wall, small channels are formed in the regions of transition between the adhesive-free zone and the peripheral zones having the adhesive strips. Through these channels and the hole in the package wall, air can get into the package from outside, particularly when there is a vacuum in the package, and the oxygen content of this air causes the oxygen-sensitive material in the package to spoil. A valve embodiment in which such leaks cannot occur is thus desirable.